Graphing Skills: Nonlinear Curves
Explore: How does slope change along a nonlinear curve?

The material presented in this problem pertains to Appendix A. This graphing exercise will calculate the slope of a nonlinear curve by drawing in a straight line tangent to the curve. Click and drag the blue diamond to the left or right--the slope of the curve is calculated and displayed in the box. Click the Open Up/Down button to change the shape of the curve

1. Click on the Open Up/Down button until the curve is open at the bottom. What is the slope of the curved line when X is 1?
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2. What happens to the slope of the line as X increases from a value of 1 to 3?
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3. What is the slope of the curved line when X is 5? How do you interpret the minus sign?
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4. What happens to the slope of the line as X increases from a value of 5 to 7?
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5. At what X value does the line have a zero slope?
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6. Experiment on your own: If the curve is getting "flatter," is the slope rising or falling? What can you say about positive and negative slopes?
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7. Click on the Open Up/Down button until the curve is open at the top. Repeat the previous questions for this graph.
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8. Comparing the "open down" and "open up" curves, speculate as to how knowledge of the slope—and how it is changing—might indicate which graph is which.
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